Another use of derivatives is to find a tangent line whose root is the same as the root of a more complicated funtion. Every approimation we make gets us closer to the actual root of the more complicated curve. This is known as Newton's Method and it's named after the man who first developed the technique, me! No, just kidding, Sir Isaac Newton developed the technique. Watch how it works here and here.
Here is a flash tutorial that explains the process we discussed in class today. You can watch Newton's Methis in action using this example. And then try these exercises to see how well you can apply what you've learned; detailed solutions are provided.